Compositional Game Theory, compositionally
Atkey, Robert and Gavranović, Bruno and Ghani, Neil and Kupke, Clemens and Ledent, Jérémy and Nordvall Forsberg, Fredrik (2020) Compositional Game Theory, compositionally. In: Applied Category Theory 2020, 2020-07-06 - 2020-07-10.
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Abstract
We present a new compositional approach to compositional game theory (CGT) based upon Arrows, a concept originally from functional programming, closely related to Tambara modules, and operators to build new Arrows from old. We model equilibria as a module over an Arrow and define an operator to build a new Arrow from such a module over an existing Arrow. We also model strategies as graded Arrows and define an operator which builds a new Arrow by taking the colimit of a graded Arrow. A final operator builds a graded Arrow from a graded bimodule. We use this compositional approach to CGT to show how known and previously unknown variants of open games can be proven to form symmetric monoidal categories.
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Item type: Conference or Workshop Item(Paper) ID code: 73674 Dates: DateEvent6 July 2020Published7 June 2020AcceptedSubjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 20 Aug 2020 14:20 Last modified: 21 Feb 2024 13:44 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/73674